Quantifying the Distortionary Fiscal Cost of 'The Bailout' - WORKING PAPER SERIES - Working Paper 2009-6
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CENTRAL BANK OF CYPRUS
EUROSYSTEM
WORKING PAPER SERIES
Quantifying the Distortionary Fiscal Cost of
‘The Bailout’
Francisco Gomes
Alexander Michaelides
Valery Polkovnichenko
December 2009
Working Paper 2009-6Central Bank of Cyprus Working Papers present work in progress by central bank staff and outside contributors. They are intended to stimulate discussion and critical comment. The opinions expressed in the papers do not necessarily reflect the views of the Central Bank of Cyprus or the Eurosystem. Address 80 Kennedy Avenue CY-1076 Nicosia, Cyprus Postal Address P. O. Box 25529 CY-1395 Nicosia, Cyprus E-mail publications@centralbank.gov.cy Website http://www.centralbank.gov.cy Fax +357 22 378153 Papers in the Working Paper Series may be downloaded from: http://www.centralbank.gov.cy/nqcontent.cfm?a_id=5755 © Central Bank of Cyprus, 2009. Reproduction is permitted provided that the source is acknowledged.
Quantifying the Distortionary Fiscal Cost of
‘The Bailout’
Francisco Gomes*, Alexander Michaelides** and Valery
Polkovnichenko***
December 2009
Abstract
We utilize an overlapping generations model with endogenous production and incomplete
markets to quantify the distortionary costs associated with financing the increase in
government expenditures directed to investments in the private sector in 2008 and 2009 (also
known as ‘the bailout’), and its differential impact on different groups of the population (in
the USA). In our baseline calibration, this distortion corresponds to a loss of approximately
$300 billion dollars in total household consumption. For plausible alternative assumptions
regarding both the expected and actual duration of this increase in expenditures, or the
willingness of foreign institutions and/or investors in absorbing additional government
debt, this number can increase to $800 billion. We find that the cost falls more dramatically
on those households which are either older and/or wealthier. Retirees face approximately
50% of the cost, as younger agents still expect to be alive when the economy has returned to
its steady-state. Across wealth groups, the top 25% of the wealth distribution bears almost
two thirds of the cost.
Keywords: Fiscal Policy, tax distortions, bailout, incomplete markets.
JEL Classification: E21, E62, G12.
_______________________
* London Business School and CEPR ** London School of Economics, Central Bank of Cyprus, CEPR and FMG
*** University of Texas at Dallas. We thank Michael Haliassos, Felix Kubler, Thomas Laubach, Fabrizio Zilibotti
and seminar participants at the University of Zurich and the Bundesbank/CFS/ECB joint lunchtime workshop
for comments and suggestions.
Correspondence: Francisco Gomes, London Business School, Regent’s Park, London NW1 4SA, UK. E-mail:
fgomes@london.edu ; Alexander Michaelides, Economic Research Department, Central Bank of Cyprus, 80
Kennedy Avenue, P.O.Box 25529, 1395 Nicosia, Cyprus. E-mail: AlexanderMichaelides@centralbank.gov.cy or
a.michaelides@lse.ac.uk ; Valery Polkovnichenko, Department of Finance and Managerial Economics, University
of Texas at Dallas, School of Management SM31, P.O.Box 830699, Richardson, TX 75083-0699, USA. E-mail:
polkovn@utdallas.edu1
1 Introduction
The years of 2008 and 2009 were characterized by unprecedented major investments on the part
of several OECD governments into private sector companies. In the USA these investments were
particularly sizeable. First, there were significant investments by the US government on an indi-
vidual basis in multiple financial firms such as Fannie May ($34B), Freddie Mac ($51B), and AIG
($70B). Second, as part of an organized effort to repair capital ratios, hundreds of banks received
substantial infusions in the form of preferred stock adding up to a total of over $200B (the TARP
program).1 Finally, there was also a non-trivial investment of $83B in the automotive industry
(GM, Chrysler, their finance arms and part suppliers), and substantial investments made by the
Federal Reserve in debt and mortgage-backed securities issued by Fannie Mae and Freddie Mac.
This set of expenditures became publicly known as ‘the bailout’.
Naturally these investments have prompted an important discussion on the costs and benefits
of such interventions. It is not the goal of our paper to offer a comprehensive evaluation of all those
costs and benefits. Our goal is a more modest yet still very important one: to provide a quantitative
assessment of one important source of costs associated with these interventions: the distortionary
impact of the changes in taxation and government debt required to finance those investments. To
the extent that our results identify distortionary costs in the order of 200 to 800 billion dollars
(in the USA), these should be viewed as one element in the computation of an overall net present
value of ‘the bailout’. If the value of all other benefits minus all other costs is less (more) than our
number, then this net present value should be viewed as negative (positive).
It is important to mention that we only consider government expenditures directly related to
investments in the corporate sector. We explicitly exclude all elements of the stimulus package
which were directly aimed at increasing household-level net worth and consumption, such as the
Economic Stimulus Act of 2008, or even the American Recovery and Reinvestment Act (which also
includes some infrastructure investments). Naturally, including these expenditures would increase
our measure of the distortionary cost, but those interventions are not so unusual in periods of reces-
sion, and here we are only interested in the less orthodox measure: government capital investments
and related expenditures.
Government investments need to be financed, either by increases in government debt or increases
in taxes, or both.2 Both of these policy options have distortionary costs on the economy, and our
1
While some major banks were allowed to repay these investments relatively quickly, the majority still remained
in the support program throughout 2009.
2
Another option, which was also used during the crisis, relies on significant increase of the money supply. This is
typically viewed as a last resort, because of inflationary fears. Most developed countries have therefore avoided this2
goal is to measure these distortions in the context of the government interventions of 2008 and
2009. We find non-trivial values for these costs. After calibrating an overlapping-generations
DSGE model with incomplete markets and heterogenous agents to the US economy we find, in
our baseline calculation, a distortionary impact of these fiscal decisions equivalent to a one time
loss of 2.75% of aggregate consumption, approximately $300 billion US dollars. Depending on the
exact assumptions on how we discount future gains and losses, the exact number changes, but very
marginally. Naturally, the magnitude of the cost will depend on the duration of the fiscal shock,
which is not currently known. As we increase the expected duration, our calculations rapidly
increase to more than 6% of annual consumption ($600 billion dollars).
Moreover, we find that the cost falls disproportionately on those households which are either
older and/or wealthier. If we equally weight the percentage consumption losses of all agents in
the economy, retirees face approximately 50% of the cost. After a few years of higher output
and consumption, due to the initial public investment, the crowding out effects start to dominate
and the distortionary effects of the fiscal expansion will still be noticeable in the economy for
approximately two to three decades. Therefore, during a significant fraction of their remaining
lives, retirees are faced with the prospect of lower capital accumulation due to the crowding out
effect of taxes. On the other hand, younger agents still expect to be alive when the economy has
returned to its steady-state, and therefore their remaining life-time wealth is less affected. If we
perform the same calculation across wealth groups, the top 25% of the wealth distribution bears
almost 2/3 of the cost. Interestingly, the impact on middle class households is relatively uniform,
regardless of whether they are stockholders or not, and not much higher than the impact on the
poorer households. This is driven by the high concentration of wealth among the right tail of the
distribution, and highlights the importance of capturing this feature of the data within the model,
a point which we will re-empashize below.
Currently, a significant fraction of US government bonds is being held by non-US investors and
institutions (e.g. other central banks). However, it is not clear how much additional US debt these
investors will be willing to absorb. Some of them have in fact already suggested that they would
not be interested in increasing their holdings much further. This is naturally one crucial element
for determining the economic impact of the fiscal expansion program, and consequently the fiscal
form of financing other than in extraordinary circumstances. Throughout 2008 and 2009, the US Federal Reserve
has substantially increased the provision of loans to companies and financial institutions and widened the range of
financial securities it accepted as collateral for those loans. It also provided financing for the bulk of the GSE-issued
mortgage-backed securities and GSE debt. In addition, the Fed supported a program of purchasing treasury debt
which began to wind down at the end of summer 2009. Later in the paper, when we calibrate the magnitude of
government intervention in capital markets, we will discuss the Fed’s expenditures in more detail.3
distortion that it implies. As we consider alternative scenarios, where foreign investors are less
willing to buy additional US bonds, the increase in domestic interest rates and the decrease in
private investment are both naturally much larger. In those settings, the total distortionary impact
is now closer to one trillion US dollars.
We conduct our analysis using a detailed DSGE model which captures reasonably well many im-
portant features of aggregate economic variables and cross-sectional behavior of households. More
precisely, we consider an overlapping-generations general equilibrium production-economy model
with incomplete markets, heterogeneous agents and limited stock market participation. A pro-
duction economy set-up is obviously crucial since we want to measure the impact of government
decisions on investment and capital accumulation. As discussed in Aiyagari (1994) or Castaneda
et al. (2003), for example, market incompleteness is crucial to match the wealth distribution in
the data with a realistic calibration of the underlying structural parameters.3 Capturing this dis-
tribution is very important for providing an accurate assessment of the household-level responses
to the fiscal policy decisions, and for allowing us to study the differential impact of fiscal interven-
tions across realistically calibrated heterogeneous groups of households (see Domeij and Heathcote
(2004)). Finally, considering an overlapping-generations model provides us with a set-up to study
the differential impact across age cohorts.4
The magnitude and importance of multiple ‘government bailouts’ across several countries has
generated a growing number of academic papers analyzing government actions in response to the
financial and economic crisis of 2008/2009. Naturally, there is an even larger literature analyzing
the causes and consequences of the financial crisis of 2008-2009, but our work belongs in the first
group. We take the financial crisis as given and analyze the distortionary impact of the government
intervention in this context.5 Existing papers have focused on alternative aspects of the stimulus,
3
In our economy markets are incomplete due to aggregate uncertainty, idiosyncratic productivity shocks and
limited stock market participation. The idiosyncratic shocks are not perfectly diversifiable due to the presence of
borrowing constraints. These are features that have been identified as important for matching quantitatively the
wealth distribution.
4
It is important to mention that, following a standard practice of neoclassical macroeconomics we do not include
an explicit financial sector in the model. It is true that a significant portion of government investments occurred in
the financial sector, but given our focus on the distortionary impact of the government fiscal intervention, it is hard
to see the benefit of modeling directly the sectors that received funding (or any bias in our analysis as a result of not
doing this), which would then also have to include the insurance and automotive sectors.
5
Not all government interventions in the private markets during the crisis were accompanied by direct capital
investments. For example, Veronesi and Zingales (2009) consider an episode which did not involve immediate
increased spending or fiscal distortions. They compute the costs and benefits of government guarantees of private
bank debts using CDS pricing data and conclude that the guarantees represented a transfer of wealth from taxpayers
to banks through the reduction of bankruptcy probabilities. However, the total effect of the intervention was positive
creating a net present value of almost $100 billion dollars.4
mostly in the US. Cogan, Cwik, Taylor and Wieland (2009), Christiano, Eichenbaum, and Rebelo
(2009) and Hall (2009) evaluate the effectiveness of economic stimulus on GDP and employment.
They compare the effects of a fiscal stimulus and reach different conclusions. Cogan et al. (2009)
conclude that the effect of the stimulus is likely to be small, while the other two papers find it to be
potentially quite large. We differ from these papers by looking at the effect of capital investments
financed by the government, not government consumption expenditures per se, and we are interested
in the distortionary impact of debt and taxes used to finance capital investment expenditures.6
To the extent that we consider the impact of tax changes, our paper complements the recent
study by Barro and Redlick (2009). They construct a marginal tax rates series for the U.S. and use
it to empirically determine how a change in the marginal tax rate affects macroeconomic variables.
They find that reducing the marginal tax rate by one percentage point raises next year’s GDP
growth by around 0.6% per year. Our quantitative experiments focussing on raising the marginal
tax rate on capital income are broadly consistent with their estimates.
The paper is structured as follows. Section 2 presents the model, the fiscal policy variables and
their behavior, while section 3 describes the calibration. Section 4 reports the baseline unconditional
results of the model economy that is being used to conduct the experiments. Section 5 presents
the responses to the fiscal expansion in the context of our baseline calibration, while section 6
considers alternative scenarios. Section 7 provides the concluding remarks. Technical details of the
computational procedure are provided in the appendix.
2 The Model Economy
The model is solved at an annual frequency. Households have a finite horizon divided in two main
phases: working life and retirement. During working life they receive a wage income subject to
uninsurable shocks, and against which they cannot borrow. At retirement they receive a pension,
financed by taxes on current workers’ wages. There are two types of agents: non-stockholders and
stockholders. The former can only invest in riskless government bonds, while stockholders can also
invest in claims to the risky capital stock (equity).
Firms are perfectly competitive, and combine capital and labor, using a constant returns to
scale technology, to produce a non-durable consumption good. The government taxes wages, capital
gains and consumption expenditures (sales) to finance government expenditures (including capital
6
For the same reason, our paper differs from the recent literature that uses structural VARs (for instance, Blan-
chard and Perotti (2002) or Ramey (2009)) or variants of new Keynesian models (for example, Gali et. al. (2007))
to analyze fiscal policy shocks.5
investments) and the interest payments on public debt. As previously discussed, and following the
standard practice in fiscal policy models, we do not include a financial sector. For the purpose of
measuring the distortionary impact of government debt and taxes we do not need to model the
financial intermediation process.
2.1 Firms
2.1.1 Production function
The technology in the economy is characterized by a standard Cobb-Douglas production function,
with total time-t output given by7
Yt = Zt Ktα Lt 1−α (1)
where K is the total capital stock in the economy, L is the total labor supply, and Z is a stochastic
productivity which follows the process
Zt = Gt Ut , Gt = (1 + g)t
Secular growth in the economy is determined by the constant g (>0), while the productivity shocks
Ut are stochastic.
Firms make decisions after observing aggregate shocks. Therefore, they solve a sequence of static
maximization problems with no uncertainty, and factor prices (wages, Wt , and return on capital,
RtK ) are given by the first-order conditions
Wt = (1 − α)Zt (Kt /Lt )α (2)
and
RtK = αZt (Lt /Kt )1−α − δ t (3)
where δ t is a stochastic depreciation rate, as discussed in the next section.
2.1.2 Stochastic depreciation
Standard frictionless production economies cannot generate sufficient return volatility, since agents
can adjust their investment plans to smooth consumption over time (see Jermann (1998) or Boldrin,
7
This is equivalent to the labor-augmenting formulation
t Lt )1−α
Yt = Ktα (Z
t )1−α , we just need to consider a different normalization factor to obtain stationary variables.
with Zt = (Z6
Christiano and Fisher (2001)). This usually motivates adjustment costs for capital, which create
fluctuations in the price of capital and increase return volatility. Since we have incomplete markets,
stockholders stochastic discount factors are not equalized, and they will therefore disagree on the
solution to the optimal intertemporal decision problem of the firm (see Grossman and Hart (1979)).
This is not a concern here because there is no intertemporal dimension to the firm’s problem, but
introducing adjustment costs would change that. Recent papers with production economies and
incomplete markets have therefore captured the effect of adjustment costs by assuming a stochastic
depreciation rate for capital (e.g. Gomes and Michaelides (2008), Storesletten et al. (2007), Krueger
and Kubler (2006), and Gottardi and Kubler (2004)). Here we follow the same route and assume
that the depreciation rate is given by
δ t = δ + s × ηt (4)
where η t is a two-point approximation to an i.i.d. standard normal, and s is a scalar. Therefore, δ t
is a general measure of economic depreciation, combining physical depreciation, adjustment costs,
capital utilization and investment-specific productivity shocks.8
2.2 Government sector
We define two different periods of government ”behavior” in our economy: normal periods and
periods of fiscal intervention. In normal periods the government simply finances government con-
sumption and interest payments on pre-existing bonds, with tax rates that are kept constant. So,
the government does not own any capital and the supply of bonds is also kept constant at a “nor-
mal” level. In periods of fiscal intervention, the government expands the supply of bonds to finance
investments in the private sector (capital purchases), and this is followed by an increase in taxes in
order to pay the interest on the additional debt. These additional investments will only occur in
response to negative economic shocks, and will persist for a while, until the government decides to
revert the bond supply (and taxes) back to the “normal” level.
2.2.1 Budget Constraint
To facilitate the exposition, let us first consider the government’s budget constraint in the absence
of governmentally-owned capital stock. In such an economy we would have
(1 + RtB )Bt + Gct = Tt + Bt+1 (5)
8
We assume that η t is uncorrelated with the productivity shock Ut since, as shown by Gomes and Michaelides
(2008), introducing (moderate) correlation between these two variables would have a negligble impact on results.7
where Gc is government consumption, B is public debt, RB is the interest rate on government
bonds, and T denotes tax revenues. Tax proceeds arise from proportional taxation on capital (tax
rate τ K ), proportional taxation on bond income (τ B ), proportional taxation on labor (tax rate τ L )
and a proportional consumption tax (tax rate τ C ).9 Labor taxes are non-distortionary in our model
because there is no household labor-leisure decision. As a result we will simply refer to them as
lump-sum taxes, which is what they effectively are.10
Now we can extend the previous budget constraint to include state-owned capital. More pre-
cisely, denoting state-owned capital by KtG , equation (5) is replaced with
(1 + RtB )Bt + Gct = Tt + Bt+1 + (1 + RtK )KtG − (Kt+1
G
− KtG ) (6)
where we take into account two additional elements. First, part of the government’s increases
(decreases) in tax rates and bonds are being used to increase (decrease) its investments in physical
capital. Second, the government also earns a return on the capital stock that it (potentially) owns.11
2.2.2 Interventions: transition probabilities
As previously discussed, in the model the government might choose to issue government bonds
to stimulate the economy, by investing the proceeds in additional capital stock. This will then
be followed by an increase in taxes to finance the interest on those bonds. Therefore, both the
tax rate on capital and the supply of government bonds are stochastic variables. Each of these
is characterized by two potential states: a “normal” state and an “intervention” state. In the
“normal” state the capital income tax rate (τ K,t ) is equal to τ K , but it can increase by ∆τ (i.e.
to τ K,t = τ K + ∆τ ) according to a set of conditional probabilities: Πτ . Likewise, bond supply
alternates between a “normal” level, (B) and a high level (B + ∆B ), based on another set of
conditional probabilities: ΠB .
In the model government interventions will only occur following negative economic shocks, so
the transition dynamics for the bond supply is a Markov Chain where the transition probabilities
9
The proportional taxation on bond income is redundant since bonds are issued by the government. Nevertheless,
since this taxation does exist in reality, we include it in the model to make the calibration more transparent.
10
It would also be interesting to study the possibility of financing the government expenditures with distortionary
labor income taxes, however this would require the inclusion of a labor supply decision, a substantial additional
complexity. In addition, as we discuss below, models with labor taxes and endogenous labor supply face an important
calibration problem, unless different complex features of the tax code are carefully modeled, making this an even
more formidable computational task. Therefore, in this paper, we only consider alternative combinations of capital
income taxes and debt as sources of financing government interventions.
11
The government is assumed to re-invest to off-set depreciation, thus keeping the value of its capital stock constant
over time.8
also depend on the realization of the stochastic depreciation shock, ΠB = ΠB (Bt+1 , Bt , η t ), and in
particular:
π B (Bt+1 = B + ∆B , Bt = B, ηt = 1) = π B
HLL > 0
π B (Bt+1 = B + ∆B , Bt = B, ηt = −1) = π B
HLH = 0
so that π B
HLL /2 effectively determines the unconditional probability of an intervention occurring.
In addition, we will also assume that the expected duration of the increase in bond supply is
independent of state of the economy following the intervention date:
π B (Bt+1 = B, Bt = B + ∆B , ηt = 1) = π B B B
LHL = π (Bt+1 = B, Bt = B + ∆B , η t = −1) = π LHH > 0
It would be trivial to change this set-up, and consider different probabilities here, but that would
add one more parameter to calibrate.
With regards to the capital income tax rate, the transition probabilities in the Markov Chain
depend on the bond supply (Πτ = Πτ (τ K,t+1 , τ K,t , Bt+1 )), since tax rates only increase in the years
following a bond issuance (to finance the additional interest payments)
π τ (τ K,t+1 = τ K + ∆τ , τ K,t = τ K , Bt = B + ∆B ) = πτHLH = 1
π τ (τ K,t+1 = τ K + ∆τ , τ K,t = τ K , Bt = B) = π τHLL = 0
and revert back to normal when government debt reverts back to B:
π τ (τ K,t+1 = τ K , τ K,t = τ K + ∆τ , Bt = B + ∆B ) = πτLHH = 0
π τ (τ K,t+1 = τ K , τ K,t = τ K + ∆τ , Bt = B) = π τLHL = 1
To summarize, across the two Markov Chains we only have two transition probabilities to cali-
brate:
1) The unconditional probability of an intervention: πB
HLL /2
2) The expected duration of the intervention (higher bonds and taxes): π B B
LHL (= π LHH )
2.2.3 Foreign-held government bonds
In the data, not all of government debt is owned by national residents. In the US, between 1970 and
2003, on average 20% of debt held by the public is held by foreign investors. While this number was
relatively stable throughout 1990’s, in the last 15 years there has been a substantial upward trend
and this percentage more than doubled. This motivates our baseline calibration of B to the actual9
percentage of bonds held by US households. However, when we increase the supply of bonds we
now need to make an assumption regarding the percentage of these new bonds that will be bought
by foreigners. In the US in particular, there is currently significant concern that this percentage will
be much lower than in the past. Therefore, while in our baseline calibration we set this percentage
(later on denoted by bF ) equal to 25%, we will also consider a scenario where this number is lower.
2.3 Households and financial markets
Households have Epstein-Zin preferences (Epstein-Zin (1991)) defined over a single nondurable
consumption good. Let Ct denote consumption in period t, then preferences are defined by
1−1/ψ
1
1−1/ψ 1−ρ
1−1/ψ
Vt = (1 − β)Ct + β Et (Vt+1 ) 1−ρ (7)
where ρ is the coefficient of relative risk aversion, ψ denotes the elasticity of intertemporal substi-
tution and β is the discount factor. Household have a finite horizon divided in two main periods:
working life and retirement.
We let i index individual households, and a denote age/cohort. The stochastic process for
i
individual labor income (Hat ) is then given by:
i
Hat = Wt Lia , (8)
where Lia (the household’s labor productivity) is a function of age. This productivity is specified
to match the standard stochastic earnings profile in life-cycle models. More precisely, labor income
productivity combines both permanent (Pai) and transitory (εi ) shocks with a deterministic age-
specific profile:
Lia = Pai εi (9)
Pai = exp(f (a))Pa−1
i
ξi , (10)
where f (a) is a deterministic function of age, capturing the typical hump-shape profile in life-cycle
earnings. We assume that ln εi , and ln ξ i are each independent and identically distributed with
mean {−.5 ∗ σ 2ε , −.5 ∗ σ 2ξ }, and variances σ 2ε and σ 2ξ , respectively.
Retirement is exogenous and deterministic. All households retire at age 65 (aR = 46) and
retirement earnings are given by: λPaiR Wt , where λ is the (exogenous) replacement ratio. The
retirement income is funded by a proportional social security tax τ s discussed later.
Households receive labor income during working life and pension payments during retirement,
and can invest in two financial assets: a one-period riskless asset (government bond), and a risky10
1
investment opportunity (capital stock). The riskless asset return is RtB = B
Pt−1
− 1, where P B
denotes the government bond price. The return on the risky asset is denoted by RtK . We assume
that households cannot borrow against their future labor income, and cannot short the risky asset.
In appendix A we formally state the household dynamic programming problem.
2.4 Equilibrium
Households are price takers and maximize utility given their expectations about future asset returns
and aggregate wages. Under rational expectations, the latter are given by equations (2) and (3):
returns and wages are determined by future capital and labor, and by the realizations of aggregate
shocks. Labor supply is exogenous, as are the distributions of the aggregate shocks. The capital
stock, however, is endogenous. Forming rational expectations of future returns and wages is, there-
fore, essentially equivalent to forecasting the future mean capital stock (from equation (3)). As
shown by Krusell and Smith (1998), for this class of incomplete market economies, it is possible
to forecast the one-period ahead aggregate capital stock extremely accurately by using its current
value (Kt ) and the state-contingent realizations of the aggregate shocks. We use this methodology
to solve for the equilibrium of the model. The definition of the equilibrium is given in appendix A
and the numerical solution method is outlined in appendix B.
3 Calibration
Households and firms make decisions on an annual frequency. The household earnings processes
and social security are calibrated from evidence based on micro-economic data (PSID), while the
other parameters are used to match several empirical moments. The government sector variables
are calibrated to match the ratios of government bonds, government expenditures and tax revenues
to GDP. The technological parameters and preference parameters are chosen to try to replicate,
as close as possible, multiple different moments such as the consumption and investment shares of
GDP, consumption volatility, wealth distribution, limited participation, and the mean and volatility
of returns.
3.1 Labor income and social security
Agents begin working life at age 20, retire at 65, and can live up to age 90. The parameters for
the household earnings processes are taken from previous studies using the PSID. More specifically,
the variances of the idiosyncratic shocks are taken from Carroll (1992): 10 percent per year for11 σ ε and 8 percent per year for σ ξ , while the parameter values for the deterministic labor income profile, reflecting the hump shape of earnings over the life-cycle, are taken from Cocco, Gomes and Maenhout (2005). For tractability we assume that the social security budget is balanced in all periods. Given a value for the replacement ratio of working life earnings (λ), the social security tax rate (τ s ) is determined endogenously. This tax rate ensures that social security taxes are equal to total retirement benefits, taking into account the demographic weights. Consistent with the empirical evidence with regards to median replacement rates from the U.S. social security system, we use a 40% replacement rate (as in Cagetti and De Nardi (2006)), which implies an endogenous social security tax (τ s ) of approximately 17.5% to maintain social security balance period by period. 3.2 Technology Capital’s share of output (α) is set to 34%, and the average annual depreciation rate (δ) is 8% to match the investment to output ratio. To match asset return volatility we set the standard deviation of the stochastic depreciation shock at 13%. The aggregate productivity shock follows a two-state Markov Chain and its unconditional standard deviation (2.5%) is chosen to match the standard deviation in aggregate output (taken from the NIPA tables, published by the BEA). The transition probability of changing states is calibrated to 0.4, to match the average duration of business cycles, and deterministic growth is set at 1% (G = 1.01) 3.3 Government sector 3.3.1 “Normal-period” parameters The aggregate supply of bonds is set to 35% of GDP, which is the average value of U.S. Treasury securities held by the U.S. public, reported by the Congressional Budget Office (from 1962 to 2003). We only include the debt held by U.S. households because in the model this number will also correspond to domestically-held debt. This ignores the interest payments on foreign-held bonds in the government’s budget constraint. However, we can simply interpret these as an additional exogenous source of government expenditures (G). Using the average historical values for both the cost of debt and total debt outstanding, this corresponds to an additional 0.6% of GDP, which has a fairly negligible impact on our baseline calibration of G. In our analysis, when we increase government debt within the model, we explicitly keep track of the total supply of bonds (rather than just the one held domestically) in the government’s budget constraint.
12
We also need to match the share of government expenditures in GDP, which is an endoge-
nous quantity in the model. This is achieved through an appropriate calibration of the tax rates.
However, even ignoring this extra constraint, the calibration of each tax rate already (potentially)
requires a compromise between matching two different features of the data: the tax rate itself or
the corresponding share of tax revenues in GDP. We compute the tax shares using data from the
Bureau of Economic Analysis from 1929 until 2006.12 For capital income taxes we set the “normal”
tax rate (τ K ) to 40%, following Trabandt and Uhlig (2006), Carey and Rabesona (2002) and Men-
doza, Razin and Tesar (1994). We discuss the calibration of the higher tax rate and the transition
probabilities in the next section.
With respect to the tax rate on labor income, the calibration decision is clear: since we do not
have a labor supply decision in the model, then these are effectively lump-sum taxes, and therefore
we want to match the revenue share, as opposed to the tax rate. As shown in table 2, a flat rate
of 10% generates tax revenues which are in line with the empirical numbers.13 Note that, our
marginal tax rate on labor income is much lower than the one faced by most households. This
result is actually very general. Quite simply, with Cobb-Douglas technology labor income as a
fraction of GDP is simply 1 − α, and with a linear tax schedule the share of labor revenues in GDP
becomes τ l (1 − α).14 Therefore, in this class of models, researchers can either match the marginal
tax rate and dramatically over-estimate the importance of labor tax revenues in the data, or match
the revenues themselves and significantly under-estimate the distortion at the margin.15
This still leaves us with one parameter left to calibrate: the tax rate on consumption. As
previously discussed we want the model to match the share of government expenditures in GDP,
so this is actually not a free parameter. We set τ C = 13% to match G/Y given the other tax rates
and the calibration of B/Y . It turns out that this number delivers total tax revenues, as a share of
GDP, which are fairly close to their empirical counterpart.
12
The BEA data does not provide a disaggregation of total personal income taxes, and therefore we combine it
with data from the IRS to compute the relative percentages of labor income and capital income taxation included
in this category.
13
As we can see from the table, the ratio of labor tax revenues to GDP has increased over time. Although in most
of our calibration we have considered long time-series as much as possible, we want the fiscal policy conditions in our
baseline economy to be fairly close to the current values, so that our results are directly applicable to the current US
economy. Therefore, here we put more emphasis on matching the 2006 value (8.71%) than the 1929-2006 average
(6.80%).
14
In our model the numbers are actually slightly different because we also have retired households.
15
This naturally reflects the multiple sources of deductions and exemptions that are not being modeled with a
linear tax schedule. These issues and trade-offs are discussed in more detailed in Castaneda et al. (2003).13
3.3.2 Intervention parameters
In our analysis we only consider government expenditures directly related to investments in the
corporate sector, and therefore exclude the stimulus package aimed at increasing household-level
net worth and consumption. Naturally, if we also include this set of expenditures the distortionary
cost would be higher, but this type of interventions are not so unusual in periods of recession, and
we are only interested in the potentially less orthodox measure: government capital investments
and related expenditures.
In the baseline version we set the percentage increase in bonds (∆B /B) to 25%, corresponding to
8.75% of GDP, and the increase in the capital income tax rate (∆τ ) to 1.5 percentage points. This
tax rate increase is determined by trial and error so that government consumption is equal across
the two scenarios, with and without intervention. To calibrate the amount of debt increase during
the intervention we aggregate investments administered in 2008-2009 through several government
programs. In our baseline calibration we take a slightly conservative approach, since some of these
programs were financed by the Treasury and others by the Federal reserve, and the former were
not immediately financed by additional debt. However, we will consider alternative scenarios in our
experiments.
We include the following items in our calculations16 : conservatorship of Fannie Mae ($34.2B)
and Freddie Mac ($50.7B); assets purchases from collapsed Bear Sterns ($26.4B); takeover of Amer-
ican International Group ($118.9B); capital infusion program for banks ($204.7B, part of TARP);
additional TARP funds for Citigroup and Bank of America ($40B); TARP funds ($83.5B) for
restructuring of automotive industry (GM, Chrysler) and affiliates (GMAC, Chrysler Financial,
autoparts suppliers). These investments amount to $558.4B or 3.9% of GDP of $14.3 trillion (as
of 4-th quarter 2007). In addition, the Federal Reserve supported Fannie Mae and Freddie Mac by
purchasing $139.8B of GSE’s debt and through the summer of 2009 purchased $776.9B of mortgage-
backed securities issued by them. While these transactions are not supported by issuing treasury
debt, they substitute the traditional function of private capital markets. Including them brings the
total government intervention to $1,479B or about 10.3% of 2007Q4 GDP. Given that we calibrate
the debt to GDP ratio to its long run average of 35%, this expansion of debt would correspond to
the ratio rising to 45.3%. We consider a somewhat more conservative calibration and assume that
outstanding debt is increased by 8.75% of GDP (25% of its current value) bringing the total debt
16
These numbers are available from the US Treasury, Board of Governors and the New
York Federal Reserve. An updated recent summary is provided on the web by CNN Money:
http://money.cnn.com/news/storysupplement/economy/bailouttracker/index.html., and as previously mentioned,
we exclude all items related to stimulus package for consumption.14
during the intervention to 43.7% of GDP. An alternative way to assess this number is to consider
that public debt has grown from 35.7% GDP in 2007Q4 to 50.2% in 2009Q2, a change of 14.5 per-
centage points.17 As previously mentioned, we calibrate the increase in debt by 8.75% of GDP, thus
attributing about 60% of the actually observed increase in debt to direct government intervention
in capital markets, which we view as a slightly conservative estimate.
As previously discussed, a substantial portion of the US national debt (about 20% in the 1990’s
and over 40% in recent years) is held by non-residents and there is a concern that this percentage
will be much lower in the future, as foreigners will be unwilling to buy as many bonds as they
have done in the past. This could result from foreign governments redirecting financial resources
to stabilize their own economies or it could be due to the benefits from diversifying into non-dollar
denominated bonds. Therefore, while in our baseline calibration we assume that 25% of the new
bonds will be bought outside of the US (bF = 25%) , we will also consider a scenario where this
number is significantly lower (bF = 10%).
Finally we still have to calibrate the transition probabilities for bonds and taxes (ΠB and Πτ ).
When describing the model we discussed a set of assumptions that impose tight restrictions on
most of these parameters. Namely, we assumed that: i) an intervention only occurs following a
negative economic state; ii) capital income taxes increase in the year following the intervention to
finance the additional interest payments; iii) tax shocks revert back to their normal level once the
same has happened to the bonds; and iv) the expected duration of the increase in bond supply is
independent of state of the economy following the intervention date. In section 2.2, we explained
how these assumptions imply several zero/one or equality restrictions on different parameters of the
transition matrices ΠB and Πτ , leaving only two free parameters to calibrate. These are:
1) the unconditional probability of an intervention (π B
HLL /2): we set this equal to 0.01 in the
baseline case, implying a 1 in 100 years probability of an intervention. In the US we could argue
that we had one or two such scenarios (now and maybe following the Great Depression), in a period
of just over 100 years, but clearly those are too few observations to infer an expected probability.
However, this variable does not play a significant role in any of our results, as long as we keep this
value relatively small, which is perfectly reasonable.
2) the expected duration of the intervention, with both higher bonds and taxes (1/πB
LHL (=
1/πB
LHH )): in the baseline case we set this equal to 5 years, but we will also consider longer lasting
interventions.
17
As reported by the US Department of the Treasury (series FYGFDPUN available from the St. Louis Fed data
wesite), debt held by the public at in 2007Q4 was $5.13T and rose by about $2 trillion to $7.17T by 2009Q2.15
3.4 Preference heterogeneity and limited participation
We consider two groups (A and B) of households in the model: stock market participants and
non-participants. In the recent data, the two groups are almost identical in size (55% and 45%
respectively, using the data from the 2001 SCF).18 However, they have very different wealth ac-
cumulation profiles: the participation rate is 88.84% among households with wealth above the
median, and only 15.21% for those with wealth below the median. In the model we treat limited
participation as exogenous for tractability reasons, but make sure that the wealth accumulation
differences are consistent with the data.19 We use ex-ante preference heterogeneity in the discount
factor and the elasticity of intertemporal substitution to endogenously generate different wealth
accumulation profiles, and we assume stockholders make up 50% of the population, consistent with
the empirical magnitudes in the U.S. economy. Type-A (non-stockholders) have a very low discount
factor (β = 0.7) and never accumulate much wealth over the life cycle, while type-B (stockholders)
have a higher discount factor (β = 0.99) chosen to match the historical risk free rate.20 There
is strong evidence that stockholders have a higher EIS than non-stockholders (see, for example,
Vissing-Jorgensen (2002)). Therefore, we assume that non-stockholders have a lower EIS in the
model as well. We pick ψ A = 0.45 to match the wealth accumulation of this group, in combination
with the discount factor. The value of the EIS stockholders is chosen to match, as close as possible,
two different moments: the volatility of consumption growth for this group, and the volatility of
the riskless rate. This gives us ψ B = 0.7 and, as we will see later, a good calibration of both of
these moments. Finally, both types have the same risk aversion coefficient (ρ = 5).
18
These numbers take into account households that participate in the stock market indirectly through pension
funds.
19
Given the low wealth accumulation of non-stockholders, a small one-time entry cost would suffice to endogeneize
the non-participation decision. For example, Alan (2006) estimates a structural participation model and finds
that a one-time entry cost equal to approximately 2-3% of average annual income explains limited stock market
participation. Gomes and Michaelides (2008) show that a one-time cost of 5% of average annual income would deter
participation for the poorer households while matching the conditional wealth accumulation of both stockholders
and non-stockholders. We leave such an entry cost out of the model to reduce the computational burden.
20
We emphasize that the quantitative results are almost identical regardless of the method we use to generate
“poor” non-stockholders. What really matters is that we replicate poor households within the model. The same
quantitative results would be obtained under alternative specifications, as long as these two groups are calibrated
to match the same heterogeneity in wealth accumulation. For example, Gomes and Michaelides (2008) consider
heterogeneity in risk aversion and EIS, with β = 0.99 for both groups, among other combinations.16
4 Unconditional baseline results
4.1 Macroeconomic variables and asset prices
Table 1 reports the main macroeconomic quantities. The shares of consumption, investment and
government expenditures and debt relative to GDP match their empirical counterparts quite ac-
curately (panel A). The empirical moments are taken from the National Accounts reported by
Bureau of Economic Analysis, from 1929 until 2007. Following Castaneda et al. (2003) we classify
75% of durable consumption expenditures as investment and 25% as consumption. Panel B shows
that the volatilities of aggregate consumption and output growth in the model (3.02% and 3.92%,
respectively) match extremely well with the ones in the data (3.28% and 4.28%, respectively).
Panel B also shows that consumption growth of stockholders is more volatile than the consump-
tion growth of non-stockholders, consistent with the empirical evidence in Malloy, Moskowitz and
Vissing-Jorgensen (2009).
Table 2 compares the different tax revenues as a percentage of GDP relative to the 2006 data
and relative to the average tax revenues over the 1929-2006 period. The tax revenues from capital
income taxation are 5.45 percent of GDP relative to 5.78 percent in the 2006 data and 5.26 percent
in the longer run average (1929-2006). Labor income and consumption tax revenues are also similar
in magnitude to the data, providing some comfort that the tax base is captured at some level by
the model.21
Table 3 reports the main asset pricing moments implied by the model, along with their empirical
U.S. counterparts. The returns series are taken from CRSP. The equity return is the real return
on the CRSP value-weighted index (including dividends), and the rate of return on government
bonds is the real return on 1-year government bonds.22 Since firms in the model are not levered,
our return on capital corresponds to the return of unlevered equity in the data. Therefore, we
adjust the moments of our return series by the average leverage of US corporations to make them
comparable with the CRSP data.23 The equity premium in the model is relatively close to its
empirical counterpart (5.23% versus 6.54%), and the same applies to the risk free rate (1.81%
21
The model does not feature progressive taxation. We view this as an interesting extension of independent interest
in the face of large changes in government debt that need to be financed by large increases in the highest marginal
tax rate.
22
We consider 1-year bonds because we have a yearly model and, in the model, government bonds are risk free
over 1 period. In the data, the average maturity for government debt has changed over time, but it is close to 5
years. The rates of return on this debt however, also include a potentially non-trivial risk premium. Nevertheless, if
we use the price series for 5-year government bonds, we would actually obtain a very similar average return (1.66%
versus 1.23%), and the main difference would be the standard deviation: 6.10% versus 3.83%.
23
Since we are implicitly assuming risk-free corporate debt, expected levered returns are computed using the simple17
versus 1.23%). Likewise the return standard deviations (respectively, 19.74% and 1.21% for equity
and bonds) are also very similar to those observed in the data.24
4.2 Cross-sectional inequality and life-cycle profiles
The combination of idiosyncratic shocks, preference heterogeneity and differences in stock market
participation status induces significant cross-sectional heterogeneity in wealth accumulation and
consumption. The model generates gini coefficients for wealth and consumption of 0.7 and 0.29,
respectively, which compare very well with 0.8 and 0.25 in the data.25 Table 4 reports the shares
of wealth held by different percentiles of the wealth distribution both in the model and in the 2001
SCF.26 Overall, the model captures relatively well the wealth distribution. In particular, it replicates
the fact that wealth below the median is negligible, while households in the top quintile hold 69%
of total assets in our economy versus 83% in the data. For stockholders, the wealth distribution
is not as skewed as in the data, since our economy does not capture the rich entrepreneurs that
dominate the top end of the distribution.27
Figure 1 plots life cycle gini coefficients of consumption. Consistent with the empirical evi-
dence in Deaton and Paxson (1994), and more recently in Krueger and Perri (2006), consumption
inequality increases with age, and is much more pronounced during retirement because a signifi-
cant fraction of the population (mostly non-stockholders) saves very little wealth during working
years, due to their high discount rate. Figure 2 plots wealth inequality over the life cycle. For
Modigliani-Miller formula:
D unlevered
requity ≡ rK
levered
= rK
unlevered
+r − rf
E K
Along the same lines, the Sharpe ratio on levered equity must be identical to the Sharpe ratio on unlevered equity,
allowing us to compute the standard deviation on the levered claim from:
rK
levered
− rf
σ Levered
K = σ unlevered
K
rK
unlevered − rf
24
The target risk-free rate volatility is about 2% rather than the historical realized volatility, since we do not have
inflation in the model.
25
The wealth gini coefficient is computed from the 2001 Survey of Consumer Finances, while the consumption gini
coefficient is taken from Krueger and Perri (2006).
26
In the SCF, wealth is defined as liquid assets net of all non-real estate loans plus real estate equity. Liquid wealth
is made up of all types of transaction accounts, certificates of deposit, total directly-held mutual funds, stocks, bonds,
total quasi-liquid financial assets, savings bonds, the cash value of whole life insurance, other managed assets (trusts,
annuities and managed investment accounts) and other financial assets. Home equity is defined as the value of the
home less the amount still owed on the first and 2nd/3rd mortgages and the amount owed on home equity lines of
credit. Debts include all uncollateralized loans (credit cards, consumer installment loans) and loans against pensions.
27
In the data, stockholders are defined as households owning stocks directly or through mutual funds either in
taxable accounts or in pension plans.18
non-stockholders wealth inequality is mostly driven by the inequality in labor income, with a strong
fanning out over the life cycle. After age 65 there is a significant decrease as they quickly run down
their limited savings. Stockholders, on the other hand, save aggressively from early on, leading to a
slight reduction in the gini coefficient in the first few years of working life. Wealth inequality then
rises from age 25 onwards as they accumulate substantial amounts of wealth. As a whole, there is
substantial wealth dispersion in the economy reflecting the differential savings behavior across the
two different groups.
5 Response to government intervention: baseline scenario
Given the reasonable empirical implications of the quantitative model, we can now use the model
to assess its implications both for aggregate and cross-sectional outcomes. We consider a scenario
similar to the sequence of events in 2007-09, where two years of bad economic shocks depleted
the aggregate capital stock. In the model, the negative stochastic depreciation shocks capture this
event. A fiscal intervention takes place in the following year, when a third consecutive negative
realization of the economic shock occurs. Results under alternative “recession” scenarios are almost
identical and are available upon request.28
5.1 Aggregate Results
5.1.1 Impulse Responses
The impulse responses are shown in figure 3. The figure plots the difference between the outcomes
of otherwise identical simulated economies with and without a fiscal expansion. In the year of the
fiscal expansion the government issues bonds, and in order to be able to absorb them households cut
down on private investment quite dramatically: aggregate private investment falls by 31.3%. The
net effect on investment is still positive, due to the large increase in public investment, and therefore
the capital stock increases.29 This leads to higher aggregate wages, while the cost of capital falls
by 15 basis points. This reduction in the cost of capital softens the pressure on the riskless rate
resulting from the large increase in bond supply. Nevertheless, the net result is still positive with
the riskless rate increasing by 6 basis points (approximately 3% of the unconditional average)30 .
28
Naturally the actual individual responses will depend on the recession scenario being considered, but the difference
between the responses with and without fiscal intervention is very similar in all cases considered.
29
The capital stock increases relative to the no-intervention case, which is what is being plotted in the figure, but
not in absolute terms.
30
These results are consistent with Laubach’s (2008) empirical estimates.19 With higher wages consumption increases, although mostly for non-stockholders, as stockholders also have to pay higher capital income taxes: the tax rate must increase to pay for the interest on the new public debt. Aggregate consumption also responds positively in the first period of fiscal intervention, being the weighted average of the stockholder and non-stockholder consumption increases. Over the next few years, with private investment being crowded-out through the distortionary higher capital tax rates, the capital stock starts falling and this leads to a mirror-image reduction in wages and non-stockholder consumption. The drop in the capital stock is associated with an increase in the cost of capital. Stockholder consumption now falls below zero as the aggregate capital drops, capital gains taxes have risen and wages have also fallen. Once the fiscal expansion is concluded, the capital stock drops by almost 0.5% due to insuf- ficient private investment. Equity returns increase significantly at this point, while wages drop. Consumption falls by about 0.2% for non-stockholders (which are almost exclusively dependent on wage income) and by approximately 0.3% for stockholders. With a high cost of capital in the economy private investment is sluggish to adjust, and as a result the recovery period takes several years. These results might seem to suggest that the best policy would be to continue with the high debt level and never revert back to the previous steady-state, but this is actually not the case. As we will show below (subsection 6.1), such a scenario would actually deliver worse outcomes for all the variables of interest that we have computed. The initial increase in interest rates might seem counterfactual, since we actually observed a significant decrease in interest rates during this period. It is important to remember that these are differences in responses across two scenarios. Actual short-term interest rates were kept low in 2008 and 2009 because the Fed decreased its target rate, among other measures. The figures simply point out that there was an upward pressure on interest rates from the real side of the economy, which is higher in the presence of government intervention. As a result, we can conclude that the Fed’s efforts to kept short-term interest rates low had to be more significant because of the fiscal bailout. Indeed, as the crisis progressed, the Fed implemented several additional measures to maintain low interest rates, such as a wider range of collateral securities accepted for loans, intervention in the short-term commercial paper markets, purchases of mortgage-backed debt and direct purchases of treasury securities. The non-linear response of the government bond interest rate is instructive of the economic mechanism behind the ’bailout’. In the first period when the government issues a large number of new bonds the interest rate has to increase to induce households to buy them. The proceeds are invested in the capital stock which becomes productive next period. This then implies a decrease
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